Solving a multilevel linear programming problems through a new constructive approach

TL;DR

This paper introduces a new constructive algorithm for solving multilevel linear programming problems by modifying existing adaptive methods and employing a range reduction map to improve decision variable control.

Contribution

It presents a novel algorithm that combines a modified adaptive linear programming approach with a range reduction map for multilevel problems.

Findings

Algorithm successfully reduces decision variable ranges.

Numerical example demonstrates effectiveness of the method.

Improves upon previous linear programming approaches.

Abstract

In this paper, an algorithm is developed to solve a multilevel mono-objective linear programming problem (ML(MO)LPP), where the constructive adaptive method of linear programming is nested. This procedure is the modified version of the SB. Sinha and S. Sinha's linear programming approach. First, we build a map that reduces the ranges of decision variables that are over control of the previous level's decision maker, depending on the chosen approach, called the range reduction map. Then, we use it to define a new sub-optimality estimate of the adaptive method for the problem under consideration. All the construction stages are carefully checked and illustrated with a numerical example.